Question

Marley was asked to solve x2 - 4x + 9 = 0 using the Quadratic Formula. She found the discriminant first and decided she did not need to continue with the Quadratic Formula. Explain in two or more sentences why Marley is correct or why Marley is wrong.

Answer 1

We have been given Marley was asked to solve
`x^2-4x+9 = 0` using the Quadratic Formula. She found the discriminant first and decided she did not need to continue with the Quadratic Formula.

We are asked to determine whether Marley is correct or not.

We know when an equation is in form
`ax^2+bx+c=0`, we can use discriminant to check for the real solutions of equation.

`D=b^2-4(a)(c)`

If
`D>0`, then the equation will have two real solutions.

If
`D=0`, then the equation will have one real solution.

If
`D<0`, then the equation will have no real solutions.

Let us find discriminant.

`a=1,b=-4\text { and }c=9`

`D=(-4)^2-4(1)(9)`

`D=16-36`

`D=-20`

Since
`-20<0`, therefore, the equation will have no real solutions, so Marley is correct.